What the highest common factor is
It is the largest number that divides into each number in the list without a remainder.
The factors of 12 are 1, 2, 3, 4, 6 and 12, and the factors of 18 are 1, 2, 3, 6, 9 and 18, so the highest common factor is 6.
Worked example
For 12 and 18 the highest common factor is 6. The lowest common multiple of the same pair is 36.
For 24 and 36 the highest common factor is 12, because both divide by 12 and nothing larger.
Where it is used
Simplifying a fraction means dividing the top and bottom by their highest common factor. 12/18 becomes 2/3.
Splitting items into equal groups without leftovers uses the same idea.
Inputs for the highest common factor calculator
Whole numbers
Two or more whole numbers, separated by commas or spaces. Negative signs are ignored and zero is not allowed.
CALCULATOR QUESTIONS
Highest common factor calculator questions
What is the highest common factor of 12 and 18?
6, because 6 divides into both and no larger number does.
Is the highest common factor the same as the greatest common factor?
Yes. UK schools say highest common factor and US schools say greatest common factor.
What is the HCF of 24 and 36?
12. Both divide by 12, and the next factor up, 24, does not divide 36.
What is the HCF of two numbers with no shared factor?
1. Numbers like 8 and 9 share only the factor 1.